the spare does not have the same sensor in it or if it is a non sensor-ed type, it is turning at a different rpm due to a different diameter. get the flat dealt with and you should be good to go. future reference, year make and model will help greatly.
Q doesn't make sense. Do you mean you put a new tire on the spare wheel? Changed a flat tire and put on the spare? Got an entirely new spare tire?
Clarify your question and include year, make, model--because every TPMS system is different.
Spares don't often get checked so when you need to use them, you find out the air pressure is down. Add air.
you probably have uneven tire pressure.